Accuracy Preserving ENO and WENO Schemes using Novel Smoothness Measurement
For computational fluid dynamics and numerical analysis, this provides an incremental improvement to existing ENO/WENO methods by reducing oscillations without sacrificing accuracy.
The authors propose new ENO and WENO schemes with a novel smoothness measurement that reduces oscillations while maintaining high-order accuracy, even near critical points. The new WENO scheme is shown to be less oscillatory than WENO5-JS and WENO5-Z in computational tests.
A novel procedure is given for choosing smoothest stencil to construct less oscillatory ENO schemes. The procedure is further used to define smoothness parameter in the non-linear weights of new WENO schemes. The main significant features of these new ENO and WENO schemes is that they are less oscillatory and achieve their relevant order of accuracy in the presence of critical points in the exact solution. It is shown theoretically as well as computationally in $L^1$ and $L^\infty$ norm. Moreover, computational results are given to show less oscillatory behavior of the new WENO scheme compared to WENO5-JS and WENO5-Z schemes.